Question

Three coin tossed together.Find the probability of:-(i) exactly two heads (ii)at least two heads (iii)at least one head and one tail (iv)no tail.​

Answer 1

Total number of outcomes=8 {HHH,HHT,HTH,HTT,TTT,TTH,THT, THH}

(i)

$= \frac{3}{8}$

(ii)

$= \frac{4}{8} = \frac{1}{2}$

(iii)

$= \frac{8}{8} = 0$

(iv)

$= \frac{1}{8}$

Answer 2

Question:-

Three coin tossed together. Find the probability of:-

• Exactly two heads
• At least two heads
• At least one head and one tail
• No tail

Given:-

Three coins are tossed simultaneously.

To Find:-

• Exactly two heads
• At least two heads
• At least one head and one tail
• No tail

Solution:-

When three coins are tossed then the outcome will be anyone of these combinations.

$\sf TTT, THT, TTH, THH. HTT, HHT, HTH, HHH.$

So, the total number of outcomes is 8.

• For exactly two heads, the favourable outcome are THH, HHT, HTH

So, the total number of favourable outcomes is 3.

We know that, Probability = $\sf \dfrac{Number~ of ~favourable ~outcomes}{ Total ~number ~of ~outcomes}$

Thus, the probability of getting exactly two heads is 3/8

• For getting at least two heads the favourable outcomes are HHT, HTH, HHH, and THH

So, the total number of favourable outcomes is 4.

We know that, Probability= $\sf \dfrac{Number~ of ~favourable ~outcomes}{ Total ~number ~of ~outcomes}$

Thus, the probability of getting at least two heads when three coins are tossed simultaneously =$\sf \dfrac{ 4}{8}$ = $\sf \dfrac{ 1}{2}$

• For getting at least one head and one tail the cases are THT, TTH, THH, HTT, HHT, and HTH.

So, the total number of favourable outcomes i.e. at least one tail and one head is 6

We know that, Probability = $\sf \dfrac{Number~ of ~favourable ~outcomes}{ Total ~number ~of ~outcomes}$

Thus, the probability of getting at least one head and one tail = $\sf \dfrac{ 6}{8}$ = $\sf \dfrac{ 3}{4}$

• For getting an outcome of no tail, the only possibility is HHH.

So, the total number of favourable outcomes is 1.

We know that, Probability = $\sf \dfrac{Number~ of ~favourable ~outcomes}{ Total ~number ~of ~outcomes}$

Thus, the probability of getting no tails is $\sf \dfrac{ 1}{8}$.

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