The probability of a tropical storm becomes a hurricane is 0.53. If the weather service predicts 6 more tropical storms, what is the probability that exactly 5 of them become hurricanes?

0.1179

Step-by-step explanation:

Given that :

p = 0.53

n = 6 ; x = 5

P(x = 5)

According to the binomial probability formula :

P(x = r) = nCr * p^r * (1 - p)^(n - r)

P(x = 5) = 6C5 * 0.53^5 * (1 - 0.53)^(6 - 5)

P(x = 5) = 6C5 * 0.53^5 * 0.47^1

P(x = 5) = 6 * 0.53^5 * 0.47^1

P(x = 5) = 0.117931129026

= 0.1179

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560