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11 May 2025, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
74% (02:25) correct
26%
(03:07)
wrong
based on 276
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Date
Time
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Not Attempted Yet
A bag contains 4 white tokens, 4 purple tokens, and 2 orange tokens. Jason is playing a game in which he pulls tokens out of the bag one at a time without replacing them. If he pulls out a white token at any point, then he loses, and if he pulls out 4 tokens and doesn’t get any white tokens then he wins. What is the probability of Jason losing the game?
A. 1/14
B. 13/14
C. 209/210
D. 81/625
E. 544/625
A. 1/14
B. 13/14
C. 209/210
D. 81/625
E. 544/625
11 May 2025, 08:25
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Probability of Jason wining the game= (6/10)*(5/9)*(4/8)*(3/7)=1/14
Probability of Jason losing the game= (1)-(1/14)=13/14
Answer: B
Probability of Jason losing the game= (1)-(1/14)=13/14
Answer: B
31 Jan 2026, 11:23
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Deconstructing the Question
The bag has 4 white tokens, 4 purple tokens, and 2 orange tokens (10 total).
Jason draws 4 tokens without replacement.
He loses if he draws a white at any point, so we want P(at least one white in 4 draws).
Use the complement:
\(P(\text{lose}) = 1 - P(\text{no white in 4 draws})\)
Step-by-step
Non-white tokens = purple + orange = \(4+2=6\).
Winning means drawing 4 tokens all from the 6 non-white tokens:
\(P(\text{win})=\frac{C(6,4)}{C(10,4)}\)
Compute:
\(C(6,4)=15,\quad C(10,4)=210\)
So:
\(P(\text{win})=\frac{15}{210}=\frac{1}{14}\)
Therefore:
\(P(\text{lose}) = 1 - \frac{1}{14} = \frac{13}{14}\)
Answer: (B) 13/14
The bag has 4 white tokens, 4 purple tokens, and 2 orange tokens (10 total).
Jason draws 4 tokens without replacement.
He loses if he draws a white at any point, so we want P(at least one white in 4 draws).
Use the complement:
\(P(\text{lose}) = 1 - P(\text{no white in 4 draws})\)
Step-by-step
Non-white tokens = purple + orange = \(4+2=6\).
Winning means drawing 4 tokens all from the 6 non-white tokens:
\(P(\text{win})=\frac{C(6,4)}{C(10,4)}\)
Compute:
\(C(6,4)=15,\quad C(10,4)=210\)
So:
\(P(\text{win})=\frac{15}{210}=\frac{1}{14}\)
Therefore:
\(P(\text{lose}) = 1 - \frac{1}{14} = \frac{13}{14}\)
Answer: (B) 13/14
