Question

In a certain game of chance, your chances of winning are 0.3. Assume outcomes are independent and that you will play the game four times. Q: What is the probability that you win at most once

Answer 1

0.6517

Explanation:

Given that in a certain game of chance, your chances of winning are 0.3.

We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)

Also there are only two outcomes

Let X be the number of games you win when you play 4 times

Then X is binomial with p = 0.3 and n =4

Required probability

= Probability that you win at most once

=
`P(X\leq 1)\\=P(X=0)+P(X=1)`

We have as per binomial theorem

P(X=r) =
`nCr p^r (1-p)^(n-r)`

Using the above the required prob

= 0.6517