A fair coin is tossed and an unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head?This question was previously asked in Show
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Answer (Detailed Solution Below)Option 3 : \(\frac{1}{4}\) Free Electric charges and coulomb's law (Basic) 10 Questions 10 Marks 10 Mins Concept The sample space when a fair coin is tossed and an unbiased dice is rolled together is as follows: (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6) (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) Total outcomes = 12 Calculation Pairs in which we get a 2 or 4 or 6 along with head are as follows: (H, 2), (H, 4), (H, 6) Total favourable outcomes = 3 Required probability \(= \frac{3}{{12}}\) \(= \frac{1}{{4}}\) Correct option is (3). Ace your Mathematics and Probability preparations for Probability of Random Experiments with us and master Problems on coins for your exams. Learn today! 1) An unbiased dice is thrown. What is the probability that the number is Even Solution: `:.n(S)=6` Let `E` = event of getting a number is even `:.E = {2,4,6}` `:.n(E) = 3` `:.P(E)=(n(E))/(n(S))=3/6=1/2` 2) An unbiased dice is thrown. What is the probability that the number is Multiple/Divide by 3 Solution: `:.n(S)=6` Let `E` = event of getting a number divide by 3 `:.E = {3,6}` `:.n(E) = 2` `:.P(E)=(n(E))/(n(S))=2/6=1/3` 3) An unbiased dice is thrown. What is the probability that the number is <= 4 Solution: `:.n(S)=6` Let `E` = event of getting a number `<=` 4 `:.E = {1,2,3,4}` `:.n(E) = 4` `:.P(E)=(n(E))/(n(S))=4/6=2/3` 4) An unbiased dice is thrown. What is the probability that the number is Prime Solution: `:.n(S)=6` Let `E` = event of getting a number is prime `:.E = {2,3,5}` `:.n(E) = 3` `:.P(E)=(n(E))/(n(S))=3/6=1/2` 5) An unbiased dice is thrown. What is the probability that the number is >= 5 Solution: `:.n(S)=6` Let `E` = event of getting a number `>=` 5 `:.E = {5,6}` `:.n(E) = 2` `:.P(E)=(n(E))/(n(S))=2/6=1/3` This material is intended as a summary. Use your textbook for detail explanation.
An unbiased dice is thrown. What is the probability of getting
Solution In a single throw of an unbiased dice, you can get any one of the outcomes: 1, 2, 3, 4, 5, or 6. So, exhaustive number of cases = 6. (i) An even number is obtained if you obtain any one of 2, 4, 6 as an outcome. So, favourable number of cases = 3. Thus, required probability = 3/6 = 1/2 (ii) A multiple of 3 is obtained if you obtain any one of 3, 6 as an outcome. So, favourable number of cases = 2 Thus, required probability = 2/6 = 1/3 (iii) An even number or a multiple of 3 is obtained in any of the following outcomes 2, 3, 4, 6. So, favourable number of cases = 4. Thus, required probability = 4/6 = 2/3 (iv) An even number and a multiple of 3 is obtained if you get 6 as an outcome. So, favourable number of cases = 1. Thus, required probability = 1/6 Solution Difference between biased and unbiased dice:In a biased die, the outcomes are not equally likely. So that the probability of coming to each face is not equal.An unbiased dice means that there is an equal probability of occurrence of any of the faces when the dice is rolled. So that, when we rolled an unbiased dice, the probability of coming to each face is equal.∴P(1)=P(2)=P(3)=P(45)=P(5)=P(6)=16Hence, In the biased die, the outcomes are not equally likely and in the unbiased die, outcomes are equally likely.How do you find the probability of a biased die?Let 0 < x < 1/6 be a real number. When a certain biased dice is rolled, a particular face F occurs with probability 1/6 − x and and its opposite face occurs with probability 1/6 + x; the other four faces occur with probability 1/6. Recall that opposite faces sum to 7 in any dice.
What is a biased 6 sided dice?A 6 sided dice is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly.
What is the probability of getting a 6 on a biased dice?On a biased dice, the probability of getting a 6 is 4/5The dice is rolled 500 times.
Can a dice be biased?A biased die is more likely to land on some faces than on others. For example, the die might not be a perfect cube, and some faces or edges might be worn down different amounts. There might be a piece of metal deliberately buried inside it at some position away from the centre, so as to weight it in one direction.
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