Combining team probabilities

I’m trying to establish what the combined probability would be for a certain event to occur, where there are 2 teams involved, and I know the probability of the event for EACH team. The event is ‘bookings’ within a football match. In addition, I’m also trying to establish what impact on the probability a third party would have (the referee), as they are a contributing factor to the event of a player being booked (shown a card).

The following is what I’m looking to establish:

1. The probability of 4+ bookings the match
2. The probability of 2+ bookings to Team A in the match
3. The probability of 2+ bookings to Team B in the match
4. The probability of 2+ bookings to Team A & 2+ bookings to Team B in the match

The following is the data that relates to the recent 5 matches played both Team A & Team B (not against each other), plus the most recent 5 matches the referee has refereed.

Team A received cards in previous 5 matches:

• Match 1 (2 bookings)
• Match 2 (1 booking)
• Match 3 (2 bookings)
• Match 4 (3 bookings)
• Match 5 (2 bookings)

So, 2 or more cards shown to Team A occurs 80% of the time (0.8)

Team B received cards in previous 5 matches:

• Match 1 (1 booking)
• Match 2 (4 bookings)
• Match 3 (2 bookings)
• Match 4 (2 bookings)
• Match 5 (0 bookings)

So, 2 or more cards shown to Team A occurs 60% of the time (0.6)

Referee cards shown in previous 5 matches (assume no team bias):

• Match 1 (1 booking)
• Match 2 (4 bookings)
• Match 3 (5 bookings)
• Match 4 (4 bookings)
• Match 5 (6 bookings)

So, 4 or more cards are shown to either team 80% of the time (0.8)

Hopefully the above makes sense. Any help would be greatly appreciated.

Regards G