Question

die has been thrown 6 times.(a)Find the probability that the number 2 appears at least once.(b)Suppose that it is given that the number 3 has appeared at least once. Find the conditiona probability that the number 2 has also appeared at least once.(c)Compare the results of part (a) and (b). Do you find the result reasonable? Why

Answer 1

a) P(rolling a 2) = 1/6

P(not rolling a 2) = 1 - 1/6 = 5/6

When the die is rolled 6 times,

P(2 appears at least once) = 1 - P(2 does not appear on all 6 rolls)

= 1 - (5/6)⁶

= 0.6651

b) It is known that 3 has appeared at least once.

P(2 appears at least once | 3 appeared once) = 1 - P(2 not appearing on the remaining 5 rolls)

= 1 - (5/6)⁵

= 0.5981

c) The result is reasonable. If we know that one outcome is not 2, then the number of possible rolls in which a 2 can come is reduced by 1. Therefore, the probability of rolling at least one 2 will be reduced in part b.