Question

The probability that a student is accepted to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 4 are accepted

Answer 1

Answer:0.849185

Explanation:

Binomial probability formula we will use:

`$P(x)=(n !)/(x !(n-x) !) p^(x) q^(n-x)$`

where,

`n=5$\\$\mathrm{P}$ (probability of success) $=0.3$\\q=1-p`

The computation of the probability will be :

`$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3)$\\$=\left[(5 !)/(5 !(5-0) !)(0.3)^(0)(1-0.3)^(5-0)\right]+\left[(5 !)/(5 !(5-1) !)(0.3)^(1)(1-0.3)^(5-1)\right]$$+\left[(5 !)/(5 !(5-2) !)(0.3)^(2)(1-0.3)^(5-2)\right]$$++\left[(5 !)/(5 !(5-3) !)(0.3)^(3)(1-0.3)^(5-3)\right]$$++\left[(5 !)/(5 !(5-4) !)(0.3)^(4)(1-0.3)^(5-4)\right]$\\$=0.1681+0.3601+0.3087+0.006615+0.00567$\\$\Rightarrow 0.849185$`

The probability that at most 4 are accepted = 0.849185