Question

13. The probability of getting at least one head when we toss 3 unbiased coins is​

Answer 1

Let's assume that H be for head and T for tail.

Total number of outcomes when three unbiased coins are tossed simultaneously:-

1. HHH,
2. HHT,
3. HTH,
4. HTT,
5. THH,
6. THT,
7. TTH,
8. TTT

In our given question, we need exact one head, which is appeared in 3 tosses: - HTT, THT and TTH. So these are the possible outcomes for exact one head.

When we tossed 3 coins, there were total 8 equally likely outcomes.

This is observed by taking the number of simultaneous outcomes(2), heads and tails, and then raising it to the power of the number of events(3), 2³ = 2×2×2 = 8

And therefore, probability for exact one head will be 3/8.

Explanation:-

Here, to calculate the probability of getting at least one head or tale, we can have to calculate the probability of getting 1 head, 2 heads and 3 heads and sum them up to get the required probability.

Answer 2

$\huge\tt{\boxed{\underbrace{\overbrace{\bold\color{blue}{❄GiVeN❄}}}}}$

• ㅤㅤㅤㅤㅤ 3 unbiased coins are tossed

$\huge\tt{\boxed{\underbrace{\overbrace{\bold\color{blue}{☛To \:FiNd☚}}}}}$

• Probability of getting one head when 3 coins are toosed simultaneously

$\huge\tt{\boxed{\underbrace{\overbrace{\bold\color{blue}{☛FoRmuLa☚}}}}}$

$\large \rm \bold {\boxed {\rm{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: p(e) = \frac{no.of \: trails}{total \: no. \: of \: trails} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$

When three unbiased coins are tossed , we get -

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ HHH

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ HHT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ HTH

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ HTT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ TTT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ TTH

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ THT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ❄ TTT

Now , we have to write the one heads when three coins are tossed.

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ⚡THT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ⚡ HTT

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ⚡TTH

By applying the formula:-

$\\ \large\rm \bold{p(e) = \frac{no. \: of \: one \: head}{total \: no. \: of \:the \: three \: coin \:tossed } } \\ \\ \\ \large \rm \bold \red{p(of \: getting \: one \: head) = \frac{3}{8} } \\ \\ \large\rm \bold\therefore{probability \: of \: getting \: one \: head \: when \: three \: coins \: are \: tossed \: is \: \frac{3}{8} }$