Question

 

For all four of these questions, a small monster collector has captured ten Bagel-type small monsters.  Each Bagel-type small monster has a 35% chance of being a Sesame Seed-subtype and a 20% chance of being a Whole Wheat-subtype.

1. What is the probability of exactly eight of the captured small monsters being Whole Wheat-subtypes?

2. What is the probability of at least one of the captured small monsters being a Sesame Seed-subtype?

3. What is the probability that there are no Sesame Seed- or Whole Wheat-subtype small monsters captured?

4. What is the probability that are at least two Whole Wheat/Sesame Seed dual-subtype small monsters captured?

Answer 1

n = 10

Probability of Sesame seed subtype = 0.35

Probability of whole wheat subtype = 0.20

a) Probability of exactly 8, P(X = 8) =

= 10!/(8!* 2!) * 0.2^8 * 0.8^2

= 0.000074

b)

Probability of at least 1, P(X ≥ 1) = 1 - P(X ≤ 0)

= 1 - 10!/(0!* 10!) * 0.35^0 * 0.65^10

= 0.9865

c)

Probability that there are no Sesame Seed- or Whole Wheat-subtype small monsters captured =

P(S or W)' = 1 - P(S or W)

= 1 - [0.20^10 + 0.35^10 + (0.20*0.35)^10)

= 0.9999723

d)

Probability of Whole Wheat/Sesame Seed dual-subtype = 0.2*.35 = 0.07

Probability that are at least two Whole Wheat/Sesame Seed dual-subtype small monsters captured =1 - P(X ≤ 2)

= 1 - [P(0) +P(1) ]

= 1 - [10!/(0!* 10!) * 0.07^0 * 0.93^10 + 10!/(1!* 9!) * 0.07^1 * 0.93^9]

= 1 - 0.4840 - 0.3643

= 0.1517