Question

The probability of getting exactly one head and one tail in two tosses of a fair coin is 0.6

We are asked to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin and it is given that the digits 0, 1, 2, 3, 4 are assigned to heads and 5, 6, 7, 8, 9 are assigned to tails.
By Making a pair of two digits the outcomes on basis of random digits are HT, HH, TT, TH, HH, HT, TT, TH, TH, HT.
Hence, the probability of head and tail = Total pairs with one head and one tail/Total number of pairs
= 6/10
= 0.6
My question is how determinate HT, HH, TT, TH, HH, HT, TT, TH, TH, HT.?

Answer 1

In order to determine the outcomes of two tosses of a fair coin using the assigned digits for heads (0, 1, 2, 3, 4) and tails (5, 6, 7, 8, 9), we need to understand the digit-to-outcome mapping and then generate all possible pairs of outcomes based on the random digits.

Given:

Heads: Digits 0, 1, 2, 3, 4

Tails: Digits 5, 6, 7, 8, 9

The combinations for one head and one tail in two tosses can be generated as follows:

H (head) can be represented by digits 0, 1, 2, 3, 4.

T (tail) can be represented by digits 5, 6, 7, 8, 9.

Using these digits to represent outcomes, we can create pairs based on all possible combinations:

HT: One digit representing head (H) followed by another digit representing tail (T).

Combinations: 01, 02, 03, 04 (representing heads) paired with 56, 57, 58, 59 (representing tails).

HH: Two digits representing heads.

Combinations: 01, 02, 03, 04 paired with 01, 02, 03, 04.

TT: Two digits representing tails.

Combinations: 56, 57, 58, 59 paired with 56, 57, 58, 59.

TH: One digit representing tail (T) followed by another digit representing head (H).

Combinations: 56, 57, 58, 59 (representing tails) paired with 01, 02, 03, 04 (representing heads).

It seems there might be a repetition in your list of outcomes (HH, HT, TT, TH, HH, HT, TT, TH, TH, HT), and it should be corrected to include all the distinct outcomes as mentioned above.

Once all possible pairs are enumerated based on the digit assignments for heads and tails, you can calculate the total number of pairs and the number of pairs that represent one head and one tail to determine the probability, as shown in your calculation (6/10 = 0.6).