Question

Q4. You have 600 small marbles in a bag which are Yellow or Red colors. You know that 20% of the marbles are the color "Red". You challenge a family member to randomly remove 5 marbles from the bag, and if there is one and only one" Red marble in the five marbles they can decide where to order take out dinner tonight. What is the probability that the family member decides where to order take out dinner tonight? (Please show formulas and calculations)

Answer 1

Let X be the number of red marbles picked from the bag.

$X\sim Bin(n,p)$

P.M.F of X

$P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}$

total number of marbles to be drawn: $n=5$

Probability of picking a red marble : $p=20/100=0.2$

$P(X=1)=\binom{5}{1}0.2^1(1-0.2)^{5-1}$

$=\binom{5}{1}*0.2^1*0.8^4$$=5*0.2*0.4096=0.4096$

Probability that the family member decides where to order take out dinner tonight is 0.4096