The probability of getting heads is three times as much as the probabi

Cariglinom5

Cariglinom5

Answered question

2021-11-16

The probability of getting heads is three times as much as the probability of getting tails, find the probability that a person flipping a coin gets
(a) the fourth head on the eighth flip;
(b) the first head on the fifth flip.

Answer & Explanation

soniarus7x

soniarus7x

Beginner2021-11-17Added 17 answers

Step 1 introduction
A coin is flipped several times.
We have to find the probability that:
a) we get the fourth head on the eighth flip.
b) We get the first head on the fifth flip.
Step 2 Data Given
The probability of head is three times the probability of getting tail.
Let, p= probability of getting head.
q= probability of getting tail.
So, p=3q
(pq)=3
p+q=1
3q+q=1
4q=1
q=14
p=34
Step 3 Calculation (a)
a) If we want to get the fourth head on the eighth flip, then , we need exactly 3 heads on 7 flips.
Probability of getting 3 heads on 7 flips =73C×p3q4
=35×(3q)3×q4
=35×27×q7
=94547. (since, q=14)
=0.057
Probability of getting fourth head on the 8th flip =0.057×p
=0.057×(34)
=0.04275
Step 4 Calculation (b)
b) To get the first head on the fifth flip, we need four tails on the first four flips.
Probability of getting four tails on the four flips =q4
=(14)4
=0.0039
Probability of getting the first head on the fifth flip =0.0039×p
=0.0039×(34)
=0.002925
Step 5 Conclusion
a) Probability of getting the fourth head on the eighth flip =0.04275
b) Probability of getting the first head of the fifth flip =0.002925

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