three unbiased coins are tossed togethere. What is the probability of getting

1) two heads

2) at least tow heads

3) no head

Question

three unbiased coins are tossed togethere What is the
probability of getting
1) two heads
2) at least tow heads
3) no head

Gursheen kaur. · Accepted Answer

When three unbiased coin are tossed together, then

the sample space obtained = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

where H means the head appears and T means the tail appears.

∴Total number of outcomes is obtained when three unbiased coins are tossed=8

Now,

a) The outcomes of the event, getting exactly two heads = HHT, HTH , THH.

∴Number of outcomes of the event getting exactly two heads by tossing three unbiased coins = 3

Thus, the probability of getting exactly two heads= $\frac{N o . o f f a v o u r a b l e o u t c o m e s}{T o t a l n o . o f o u t c o m e s} = \frac{3}{8}$

b) The outcomes of the event, getting at least two heads = HHT, HTH , THH, HHH

∴Number of outcomes of the event getting at least two heads by tossing three unbiased coins = 4

Thus, the probability of getting at least two heads= $\frac{N o . o f f a v o u r a b l e o u t c o m e s}{T o t a l n o . o f o u t c o m e s} = \frac{4}{8} = \frac{1}{2}$

c) The outcomes of the event getting no heads = TTT.

∴Number of outcomes of the event getting no heads by tossing three unbiased coins = 1

Thus, the probability of getting no heads= $\frac{N o . o f f a v o u r a b l e o u t c o m e s}{T o t a l n o . o f o u t c o m e s} = \frac{1}{8}$

three unbiased coins are tossed togethere. What is the probability of getting 1) two heads 2) at least tow heads 3) no head

three unbiased coins are tossed togethere. What is the probability of getting

1) two heads

2) at least tow heads

3) no head