Question

a coin is tossed 10 times with 4 times heads and 6 times tails find the probability of getting no head.​

Answer 1

Answer:

To begin with, we calculate the total number of possibilities that arise from tossing a coin 6 times . On each toss , we have 2 possibilities - a head or a tail. This gives us

2*2*2*2*2*2 = 64 possibilities

Now let's list out the desirable outcomes.

Having 4 heads

H H H H T T - This is one example of the above outcome. Something like

H H H T H T would also be equally likely and would be a desirable outcome. Thus to calculate all such permutations

6!/4!∗2!=15ways

Here , 6 is the total number of objects while 2 and 4 are the total number of identical objects.

2. Having 5 heads

H H H H H T- The total number of permutations with this mixture of heads and tails is

6!/5!∗1!=6

3. All 6 heads

- There happens to be only one way in which such a mixture can be arranged.

So therefore , calculating the probability

No of desired outcomes / No of total outcomes

15+6+1/64=11/32

0.343