Question

On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.

1. Explain why – 0.41 cannot be the probability of some event.

2. Explain why 1.21 cannot be the probability of some event.

3. Explain why 120% cannot be the probability of some event.

4. Can the number 0.56 be the probability of an event? Explain.

Answer 1

In the event of tossing a coin with 0.5 probability of each head and tails

if we toss the coin twice we have 4 possible outcomes that are equally likely

THOSE ARE (H,H), (T,H), (H,T), (T,T)

SO if we get a head on the first toss we can get (H,H) OR (H,T) WITH PROBABILITY 0.5 EACH

so NO  we are not guaranteed to get tails on the second toss

A)

-0.41 can not be a probability as it violets the amiom of probability that says probability > or equal to 0.

ALSO PROBABILITY IS DEFINED OF AN EVENT .

B)

probability of an event can NEVER be strictly greater than 1 , here 1.22 is not possible as this would imply that a certain event has 122% chances of occurring that is meaningless.

C)

SIMILAR REASON AS OF B)

probability of an event can NEVER be strictly greater than 1 , here 1.22 is not possible as this would imply that a certain event has 120% chances of occurring that is meaningless. ALSO 100% CHANCES MAKES IT A SURE EVENT.

OR IN THE FUNDAMENTAL MANNER PROBABILITY IS A RATION OF FAVORABLE TO TOAL POSSIBLE OUTCOMES THAT ARE EQUALLY LIKELY SO THE WAY IT IS DEFINED IT CAN NEVER BE MORE THAN 1

D)

YES THE PROBABILITY OF AN EVENT CAN BE 0.56 OR EVEN ANY REAL NUMBER IN [0,1] BOTH INCLUSIVE

YES FOR EXAMPLE

consider a bag having chips numbered 1 to 100 here a chip is chosen randomly

here probability of getting chip less than or equal to 56 is 56/100 that is 0.56.