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Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

  • 1/3
  • 1/6
  • 1/2
  • 1/8

Answer: Option C

Explanation:

Total cases are = 2*2*2 = 8, which are as follows
[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]

Favoured cases are = [TTH, THT, HTT, TTT] = 4

So required probability = 4/8 = 1/2

Similar Questions :

1. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is

  • 1/13
  • 2/13
  • 1/26
  • 1/52

Answer: Option C

Explanation:

Total number of cases = 52
Favourable cases = 2

Probability = 2/56 = 1/26

2. In a throw of dice what is the probability of getting number greater than 5

  • 1/2
  • 1/3
  • 1/5
  • 1/6

Answer: Option D

Explanation:

Number greater than 5 is 6, so only 1 number
Total cases of dice = [1,2,3,4,5,6]

So probability = 1/6

3. A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

  • 30%
  • 35%
  • 40%
  • 45%

Answer: Option B

Explanation:

Let A = Event that A speaks the truth
B = Event that B speaks the truth

Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5

P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5

Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%

4. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?

  • 3/4
  • 1/4
  • 7/4
  • 1/2

Answer: Option A

Explanation:

Total number of cases = 6*6 = 36

Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27

So Probability = 27/36 = 3/4

5. Two unbiased coins are tossed. What is probability of getting at most one tail ?

  • \begin{aligned} \frac{1}{2} \end{aligned}
  • \begin{aligned} \frac{1}{3} \end{aligned}
  • \begin{aligned} \frac{3}{2} \end{aligned}
  • \begin{aligned} \frac{3}{4} \end{aligned}

Answer: Option D

Explanation:

Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.

So probability = 3/4

Read more from - Probability Questions Answers
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