Question

Coin Tossing. When a dime is tossed four times , there are the following 16 possible outcomes.

Here, for example, HTTH represents the outcomes that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events.

A = event exactly two heads are tossed,

B = event the first two tosses are tails,

C = event the first toss is heads,

D = event all four tosses come up the same.

Short answer

A = Potential outcomes are TTHH, HTHT, THHT , HTTH, THTH, HHTT

B = Potential outcomes are TTHH, TTHT, TTTH, TTTT

C = Potential outcomes are HHTH, HTHH, HHHT, HTHT, HHHH, HTTH, HHTT, HTTT

D = Potential outcomes are HHHH, TTTT

Step-by-step solution

. Given information

When a dime is tossed four times, the following results are attainable.

HHTH, HTHH, THHH, TTHH

HHHT, HTHT, THHT, TTHT

HHTH, HTTH, THTH, TTTH

HHTT,HTTT, THTT, TTTT

Step 2. Utilized principle and Equation

The probability of an event lie between 0 to 1 and both are applicable.

Probability of an event is: $P\left(E\right)=\frac{No.ofoutcomesofE}{Outcomesinsamplespace}$

Step 3. Calculation

It is provided that the dime is tossed four times.

A = event exactly two heads are tossed

Potential outcomes are TTHH, HTHT, THHT , HTTH, THTH, HHTT

B = event the first two tosses are tails

Potential outcomes are TTHH, TTHT, TTTH, TTTT

C = event the first toss is heads

Potential outcomes are HHTH, HTHH, HHHT, HTHT, HHHH, HTTH, HHTT, HTTT

D = event all four tosses come up the same

Potential outcomes are HHHH, TTTT