Question

when four coins are to simultaneously what is the probability of getting 1.No head 2. No tail 3. exactly two heads​

Answer 1

Given, four coins are tossed simultaneously

Here, H = head and T = tail

So, there are 16 possible outcomes

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.

1. Probability of getting no head is:

The number of favorable outcomes: 1 (which is TTTT)

The total number of outcomes: 16

Probability = $\frac{Number of favorable outcomes}{Total number of possible outcomes}$

So, probability of getting no head is $\frac{1}{16}$.

2. Probability of getting no tail is:

The number of favorable outcomes: 1 (which is HHHH)

The total number of outcomes: 16

Probability = $\frac{Number of favorable outcomes}{Total number of possible outcomes}$

So, probability of getting no tail is $\frac{1}{16}$.

3. Probability of getting exactly two heads is:

The number of favorable outcomes: 2 (which are HHTT, TTHH)

The total number of outcomes: 16

Probability = $\frac{Number of favorable outcomes}{Total number of possible outcomes}$

So, probability of getting exactly two heads is $\frac{2}{16}$ which is $\frac{1}{8}$.