Answer:
The probability that it takes Zaylee 3 surveys or less to win for the first time = 0.06
Step-by-step explanation:
This is a negative binomial distribution problem. A negative binomial distribution problem describes a sequence of trials, each of which can have two outcomes (success or failure). We continue the trials indefinitely until we get r succeses.
The probability of y trials before obtaining r successes is given as
P(y) = ʸ⁻¹Cᵣ₋₁ pʳ qʸ⁻ʳ (for all y ≥ r)
p = probability of success
q = probability of failure
r = number of successes required
y = number of trials required
For this question
p = 2% = 0.02
q = 1 - p = 1 - 0.02 = 0.98
r = 1
y = 3 surveys or less = ≤ 3
P(y ≤ 3) = P(y=1) + P(y=2) + P(y=3)
For P(y=1)
r = 1, y = 1
P(y=1) = 1 × (0.02)¹ (0.98)¹⁻¹ = 1 × 0.02 × 0.98⁰
= 0.02
For P(y=2)
r = 1, y = 2
P(y=2) = ¹C₀ (0.02)¹ (0.98)²⁻¹
= 1 × 0.02 × 0.98 = 0.0196
For P(y=3)
r = 1, y = 3
P(y=3) = ²C₀ (0.02)¹ (0.98)³⁻¹
= 1 × 0.02¹ × 0.98² = 0.019208
P(y ≤ 3) = P(y=1) + P(y=2) + P(y=3)
= 0.02 + 0.0196 + 0.019208 = 0.058808 = 0.06 to the nearest hundredth
Hope this Helps!!!
